Fitting nonlinear low-order models for combustion instability control

Tools for fitting low-complexity nonlinear models based on experimental data are examined through the example problem of finding a reduced-order model suitable for control of a combustion instability operating in a limit cycle. This proceeds in four parts; physical modeling, linear system identification, nonlinear analysis, and validation test design. It is shown how the nonlinear tools of describing functions, bifurcation methods and manifold analysis assist in developing a simple nonlinear model capable of describing the data and consistent with physical understanding. The system being modeled is a lean gas turbine combustor which exhibits a sustained mid-range (100–1000 Hz) limit cycle instability. The closed-loop experimental data does not contain a sufficiently rich spectrum for confident modeling in the first linear system identification phase. Despite the paucity of information quality, a grey-box nonlinear model is created and parametrized which provides an explanation both of the limit-cycle fundamental oscillation and of a high frequency nonharmonic signal also present. The model structure is explored and various operating conditions simulated to understand the model better.

The validation and/or refinement of this model is then considered. The model validation problem is important because of the poor information content of the periodic limit cycle data. The challenge is to provide a practically feasible, small excitation to the loop to improve identifiability and to provide qualitative tests of model performance. We examine this problem by considering the nonlinear dynamics of the model class and feasible excitation mechanisms.